# [OPE-L:5601] RE: [OPE-L:5567] Re: Luxury Goods and Profit Rate

andrew kliman (Andrew_Kliman@CLASSIC.MSN.COM)
Wed, 8 Oct 97 16:33:51 UT

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A reply to Alejandro Ramos's post identified as follows (good idea, Ale!):

From: owner-ope-l@galaxy.csuchico.edu on behalf of aramos@aramos.bo
Sent: Wednesday, October 08, 1997 12:54 AM
To: OPE-L@galaxy.csuchico.edu
Cc: Multiple recipients of list
Subject: [OPE-L:5601] RE: [OPE-L:5567] Re: Luxury Goods and Profit Rate

Ale: :This is a math problem but if P1 = 0, corn is actually a "free
commodity", like "air" or "sunheat". So, I dont see the economic meaning of an
equation defining the "profit rate" of such use-value. (What is the profit
rate of "air production"?)"

I agree that the profit rate is meaningless when both value invested and value
received equal zero. This is important, because it reminds us that in an
equation such as

4*Pc*(1+r) = 6*Pc

r = .5 is not necessarily the solution. Dmitriev's alleged disproof of Marx's
claim that profit rests on exploitation of workers commits the simple error of
assuming that the price in this kind of case is nonzero, i.e., that things
produced without human labor have a positive price. But that is precisely
what he needed to prove, not assume.

Your parenthetical question is a truly profound one, I think. It calls into
question the whole concept of "production" employed in the "physical
quantities approach," i.e., the attempt to model economies in "objective"
terms without regard for social relations. From the standpoint of inputs
relative to outputs, air production is certainly production. From the
standpoint of inputs relative to outputs, whether the inputs and/or outputs
are property doesn't matter, and whether human labor mediates the
transformation of inputs into outputs doesn't matter. Thus we have two
proponents of the physical quantities approach, Dmitriev and Samuelson, who
apply the simultaneist equations to cases of self-reproducing machines and
wild rice on land that no one owns, respectively, and who compute profit rates
in these cases. Other proponents of the physical quantities approach tell us
that the equations apply just to cases in which everything is produced by
human labor. But the funny thing is that they employ THE SAME EQUATIONS. The
equations don't care about how anyone interprets them, and there's nothing in
the equations that makes one interpretation more valid than the other. The
whole thing lacks secure grounding of concepts. The consequences of this
problem are things like this: within the physical quantities approach,
neither those who say you need surplus labor to have profit nor those who deny
it can prove their case. Not a minor issue.

BTW, air is not only produced, it is also a BASIC commodity. What can be
produced *without* air as an input?

Ale: "Maybe in "details" like the self-reproducing non-basics what you are
saying is reasonable. But Sraffa's way to criticise the economic theory is
also a theoretical *representation of capitalism* different from that holds by
the neoclassical orthodoxy."

Only to a slight extent, having to do with "commodities" producing
"commodities" instead of "factors" producing "products." Sraffa was taken
seriously precisely because the critique was *internal*. The equations may
not look like neoclassical equations at first glance, but they are in fact
just special cases of neoclassical equations. Frank Hahn has shown this. It
is this feature that prevented the neoclassicists from just dismissing the
whole critique.

Don't be misled by the lack of "margins," i.e., substitutability and
differentiability. Those things are not crucial to neoclassicism. The Sraffa
equations are extremely similar to WALRAS' equations; Walras also had fixed
technical coefficients and, in fact, the term "technical coefficients" comes
from him. Indeed, Sraffa's positive-profit equations are easily rewritten as
Walras' zero-profit equilibrium equations, once you take into account the
difference between discounted and undiscounted prices.

Ale: "His theoretical framework is aimed to stress the "distributive
struggle" (if you like the "class struggle") between capitalists and workers
regarding the net product. In this sense, PCMC does propose a "theoretical
system or model", in a very general sense, alternative to the dominant
apologetical neoclassical construction."

Well, a lot of "Sraffians" have told us a lot of stories about the
distributive struggle determining everything, but it simply is not there in
PCMC. If I remember, there's one passing remark about the central bank
perhaps being able to set the rate of profit exogenously.

Now, as I noted, these equations are essentially neoclassical equations, so
the underdetermination in Sraffa's equational system is also present in the
neoclassical system. Sraffa goes no further; he does not attempt to theorize
the economic relations, missing from his equations, which, in reality, give us
profit rates of this level and not that level. He instead examines the
properties of the wage rate/profit rate tradeoff. Any neoclassicist could do
the same. But some of them have gone further and solved the system by means
of particular assumptions concerning economic relations, assumptions that have
nothing to do with "class struggle" -- though the wage rate/profit rate
tradeoff that Sraffa finds is of course still present. IN OTHER WORDS, THEY
SOLVE THE "SRAFFA SYSTEM" WITHOUT RECOURSE TO "CLASS STRUGGLE."

As Joan Robinson herself noted, Sraffa gives us half of an equilibrium system.
It is underdetermined; it lacks closure. My point is that it can be closed
in MANY DIFFERENT POSSIBLE ways: "class struggle," or specification of
initial endowments and time-preferences, or exogenous determination of the
profit rate by an all-powerful central bank, or Ajit telling everyone what
their distributive shares will be, etc., etc.

*However* one decides to close it, one is merely specifying the point on the
wage rate/profit rate curve that the economy is actually "on." The closure of
the system does not abolish the wage rate/profit rate tradeoff. So that
tradeoff is always present, even in neoclassical theory. To see this in
another way, assume a constant-returns-to-scale technology, or zero-profits in
the neoclassical sense. Then, neoclassical theory itself tells us that the
sum of distributive shares equals one. So if we have "capital" and "labor",

(interest share) + (wage share) = 1

so that

(interest share) = 1 - (wage share)

How's that for "class struggle"?! And it's linear, just like the standard
relation :-). Of course, this isn't exactly the same tradeoff that Sraffa
looks at, but it's close. But this tradeoff tells us no more than what is
obvious, something that everyone has always known and accepted, namely that at
a *moment in time*, you've got a fixed pie and, therefore, if someone gets a
larger slice, everyone else gets less. This is some kind of "alternative
vision"?

I don't mean to imply that Sraffa accomplished nothing. He's got the
reswitching result. More importantly, he damaged the notion that distributive
shares are explained by "returns to productive factors." The neoclassicists
had been using a variant of Austrian models, in which there's a one-way road
from "factors" to "products," which Sraffa replaced with a circular system in
which "commodities" produce "commodities." I don't yet understand very well
the impact this had, or why (can anyone explain this? Gil?), but from what I
understand, it forced general equilibrium theory out of the business of
talking about "factor shares" in the old way -- e.g., out of trying to
determine a uniform rate of interest, and into a notion of a variety of "own
rates of return" on different productive assets that won't generally be equal.
My point is only that the *wage rate/profit rate tradeoff* is no big deal.
It may have done damage to certain things certain individuals said or thought,
but no damage to neoclassical theory.

Yet I actually doubt anyone ever disputed the existence of this tradeoff.
Keep in mind that it is a completely static notion. The claims made by
trickle-down theories are dynamic -- give the capitalists more profits now so
they'll save more, which will lead to more investment, which will yield more
corn, so the workers can also get more in the future. Nothing in Sraffa
negates this in any way. The only three ideas I know of that damage this are
(1) the split between saving and investment that Keynes emphasized, (2)
investment in labor-saving techniques that reduce labor demand, and (3) Marx's
schema of expanded reproduction, which show that the new investment can go to
produce ever more machines instead of trickling down as more consumption goods
in the future. (Someone on this list [Rieu?] has noted that Steedman or